A soliton is a non-linear object which moves through space without dispersion at constant speed.
They occur naturally as solutions to the Korteweg - de Vries equation. They were first observed by
John Scott Russell in the 19th century and then by Martin Kruskal and Norman Zabusky (who
coined the term soliton) in a famous computer simulation in 1965. Insight into solitons can
be obtained by noting that the Korteweg - de Vries equation satisfies D’Alembert’s
solution:
We see at once that this satisfies two important criteria: it has a constant velocity c, and it
can also be shown that the two functions f and g can collide without altering shape.
Solitons also occur in non-linear optics and as solutions to field equations in quantum field
theory.
